If y, = u1 (t) cos(5t) + u2(t) sin(5t) is a particular solution of the differential equation y" + 25y = sec(5t) tan(4t), then us (t) = %3D Select one: 1 In cos(5t)| 25 1 In cos(5t)| 25 1 t+ tan(5t) 25 O none of the given answers is true 1 tan(5t) 25 O 1 -

Q: Solve the following initial-value problem: y'+ (tan x)y=cos²x; y(0) = − 1 - O y=−(sinx)(sin x−1)-co…

A: We will find the required.

Q: The solution of the differential equation 5/1 – x2 ? dy dx 7/1 - y? = 0 is - 5 sin-x – 7 sin-y = C 5…

A: Question is solved.

Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

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Q: The standard form of the following linear differential equation sec(x) y' + csc(x) y = 1 is: O…

A: Option A

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Q: Consider the following differential equation to be solved by variation of parameters. y" + y = sec…

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Q: Write down the form of a particular solution to the equation y" + 2y + 2y = 5e¯* sin(t) + 5t³…

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Q: Find a particular solution y, of the differential equation: (a) 2y" + 4y' + 7y = x2 (b) y" + 9y = 2…

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Q: Solve the following Second Order Differential Equation y"+2y'+ y = sin (2t)

A: # Given ODE  is       y''+2y'+y=sin 2t‐‐‐‐1

Q: Solvecos (2) O a. O b. 2 с. d. y cos Y I - [2 in (2) + co. (:)]* - = 0 dz y sin () = c C = сх ysin…

A: Given differential equation is yxcosyx-xysinyx+cosyxdydx=0       (1) Simplifying (1), we get…

Q: State the order of the given ordinary differential equation. (sin 8)y"" - (cos 8)y' = 2 Determine…

A: Part 1: Given the ordinary differential equation,                                               (sin…

Q: werty that the indicated function() explicit solution of the given first-order differential 2y² = y²…

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Q: The equation ? + sin(xy) + C = 0 is the general solution of O y' + cos (xy) = 2 (x + y) 2 (ydx +…

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Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA.…

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Q: Solve the differential equation by variation of parameters. y"+y = n²(x) xx) = c₂cos(x) + csin(x) +…

A: The solution is given as

Q: c) i) Find 2 sin cos (1 + sin 8)³ 1) Solve the differential equation sin 2x cos² y (1 + sin x)³ IL…

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: Find the general solution of the differential equation y" - 6y +25y = 0. 3x ○ y = c1e³* + c2₂eª ○…

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Q: 3. Solve y' + cos(r)y = 2 cos z subject to the initial condition that y() = 2.

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Q: the solution to the given equa y" + y' – 2y = cos(x) – 3 sin(: -

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the general solution for the following differential equation: yey cos(-7x) - 2ery sin(-7x) - 9x…

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Q: Solve the following differential equation, (s x)+(cos x) y = 3 sin x with the initi al dx condition…

A: Given differential equation is (sin x)dydx + (cos x)y = 3sin x

Q: y"+4y=x² sin 2 u

A: See the attachment

Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.